Derivation of Langevin dynamics in a nonzero background flow field

Molecular dynamics is becoming more important to study the interaction of micro and macro scales. In fluid dynamics, the multi-scale approach often leads to analyzing or simulating the molecular system in a background flow field at constant temperature. Simulation based on stochastic Langevin molecular dynamics is an alternative for ergodic sampling at constant temperature. Langevin dynamics has been derived from different micro models: for instance in [G.W. Ford, M. Kac and P. Mazur, J. Math. Phys. 6 (1965), 504-515] and [R. Zwanzig, J. Stat. Phys. 9 (1973) 215-220] from a Hamiltonian system with a heavy particle coupled through a harmonic interaction potential to a heat bath particle system, where the stochasticity enters through Gibbs distributed initial heat bath configurations, and in [D. Dürr, S. Goldstein and J.L. Lebowitz Commun. Math. Phys. 78 (1981) 507-530] from a heavy particle colliding with an ideal gas heat bath, whose the initial particle configuration is described by a Poisson field. This highlight paper makes an important contribution to derivations of Langevin dynamics by extending the ideal gas model to non vanishing background flow.

Derivation of Langevin dynamics in a nonzero background flow field
Matthew Dobson, Frédéric Legoll, Tony Lelièvre and Gabriel Stoltz
ESAIM: M2AN 47 (2013) 1583-1626
DOI: http://dx.doi.org/10.1051/m2an/2013077